York City dumped League Two Rotherham United out of the FA Cup after a sensational second-half display at Bootham Crescent.

Three goals in 13 minutes – one from Chris Smith and a Michael Rankine brace – booked the Minstermen a second round trip to Blue Square Bet Premier rivals Darlington a week on Saturday with the shell-shocked Merry Millers unable to muster anything in response.

City also struck the crossbar through Danny Racchi during their goal spree and, by the end of the game, could even afford to give Levi Mackin his first run out since suffering knee ligament damage on the opening day of the season.

City made three changes to the side that started Sunday’s 1-1 home draw with Wrexham.

Centre-back Greg Young dropped to the bench with captain Chris Smith back from suspension.

Ineligible loan signings Ashley Chambers and Robbie Weir were also replaced by the fit-again Jonathan Smith and Chris Carruthers, who earned his first start since suffering a knee injury in August.

Former City goalkeeper Andy Warrington was missing for the Millers, meanwhile, after attending the birth of his new baby and the visitors also received another blow in the pre-match warm-up, losing skipper Ryan Cresswell after the recurrence of a back injury.

The Minstermen started brightly with Daniel Parslow going close to a goal of the season contender in the sixth minute.

Picking the ball up on the half-way line, the City right-back embarked on a terrific run into the visitors’ penalty box only to produce a defender’s finish when he lifted his eight-yard shot over the bar with only Annerson to beat.

Carruthers then tested Rotherham’s rookie goalkeeper with a curling free-kick into the six-yard box, which Annerson flapped at before gathering at the second attempt.

Lone central striker Rankine and Racchi also saw edge-of-the-box efforts deflected wide, but several other first-half forays upfield broke down frustratingly with players carelessly straying offside.

While losing out in the first-half possession stakes, Rotherham still looked decisive and sharp in final third of the pitch and might have taken the lead on three occasions before the interval.

On 25 minutes, Mark Bradley’s ball into the penalty box was excellently cushioned into the firing range of Stephen Brogan by Ryan Taylor’s head but the Town midfielder’s low shot rebounded back off Michael Ingham’s left-hand post.

Djoumin Sangare was then caught napping at a throw-in, allowing Taylor to reach the byline and tee up another chance for Brogan that he fired wide of an inviting net.

Two minutes before the break, the country’s leading marksman Adam Le Fondre also broke clear on Ingham’s goal but shot wastefully into the David Longhurst Stand.

City started the second half in the ascendancy with Jonathan Smith charging on to a Sangare through ball.

After rounding Annerson, though, he decided the angle was too tight to shoot and pulled the ball back for Rankine, who could not aim his shot through a forest of covering defenders.

At the other end, the impressive Taylor headed into the side-netting and then fired inches wide after turning swiftly 20 yards from goal.

It was left to Chris Smith, though, to trigger a sensational finish to the game on 66 minutes.

The former Tamworth defender sent a powerful downward header past Annerson from Rankine’s left-footed cross after staying in the penalty box following Jonathan Smith’s cleared corner.

A second was added four minutes later when Rankine won the ball in the air and substitute Jamal Fyfield was brought down by Ashworth as he charged through on goal.

The reliable Rankine then produced an almost carbon copy penalty-kick of the one he despatched against Wrexham at the weekend, sidefooting firmly to Annerson’s left as the Rotherham goalkeeper dived to his right.

After Racchi hit the bar with a free-kick, Rankine then added a third for rampant City on 79 minutes, collecting the ball from Fyfield before working his way into a shooting position and finding Annerson’s bottom left-hand corner with a composed finish.

Match facts

York City 3 (Chris Smith 66, Rankine pen 70, 79), Rotherham United 0

York City: Michael Ingham 7, Daniel Parslow 8, David McGurk 8, Chris Smith 8, James Meredith 8, Djoumin Sangare 8, Jonathan Smith 8, Danny Racchi 8, David McDermott 8, Chris Carruthers 8, Michael Rankine 9.

Substitutions: Jamal Fyfield (for Carruthers 62, 8), Neil Barrett (for McDermott 78), Levi Mackin (for J Smith 88).

Subs not used: David Knight, Greg Young, Jamal Fyfield, Michael Gash, Leroy Constantine.

Key: 10 – Faultless; 9 – Outstanding; 8 – Excellent; 7 – Good; 6 – Average; 5 – Below par; 4 – Poor; 3 – Dud; 2 – Hopeless; 1 – Retire.

City’s star man: Michael Rankine – set up first goal, scored the two others, always a handful throughout.

Rotherham United: Jamie Annerson, Johnny Mullins, Luke Ashworth, Nick Fenton, Tom Newey, Marcus Marshall, Mark Bradley, Nicky Law, Stephen Brogan (Kevin Ellison 75), Adam Le Fondre, Ryan Taylor.

Subs not used: Danny Harrison, Jason Taylor, Jamie Green, Oliver Banks, Paul Warne, Tom Elliott.

Yellow cards: Newey 76.

Red cards: None.

Shots on target: City 4, Millers 2.

Shots off target: City 5, Millers 6.

Corners: City 5, Millers 6.

Fouls conceded: City 7, Millers 12.

Offsides: City 7, Millers 1.

Referee: David Coote (Newark).

Attendance: 2,644 (377 from Rotherham)